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The days

According to the first chapter of Genesis (including the first few verses of the second chapter), God (in the form of the plural Elohim) created the world in six days (Hebrewyom), before resting on the seventh.
Created on each day were:

The account in chapter 2

In contrast to the chronological arrangement of chapter 1 (up to verse 4 of chapter 2), chapter 2 describes in greater detail the creation of man and the Garden of Eden.

Some believe that in chapter two, creation appears to take only one day (yom, cf verse 4), with man apparently being created before the plants have grown, and before the animals are created, or at least before they are brought before Adam. Those who take this view usually believe that this apparent contradiction is evidence that the two chapters originated as two separate accounts.

Others see no lack of harmony among the accounts, but believe chapter two is intended to show the sixth day of creation from the view of man in the garden. It is also argued that the word 'formed' in verse 19 can legitimately be read as 'had formed' (as used in the NIV translation). Indeed, in that case with the garden (plants) already existing before man and animals already having been formed, but merely being brought before Adam, there is no contradiction at all. This can be seen more clearly when verse 19 is read in context:

And the LORD God said, [It is] not good that the man should be alone; I will make him an help meet for him.

And out of the ground the LORD God formed every beast of the field, and every fowl of the air; and brought [them] unto Adam to see what he would call them: and whatsoever Adam called every living creature, that [was] the name thereof.

And Adam gave names to all cattle, and to the fowl of the air, and to every beast of the field; but for Adam there was not found an help meet for him.Genesis 2:18-20 (KJV)

Furthermore, even those that propose that the two chapters began as two separate accounts accept that the two have been together in the Bible for thousands of years.
Yet for most of that time, the vast majority of believers have seen no discrepancy.
Jesus himself quoted from both chapters at the one time, showing that he didn't see them as two contradictory accounts.
This points to the only discrepancy being an imagined one.

Sources

Cruden, A., Complete Concordance to the Old and New Testaments (Lutterworth, 1930)